In time series context, let $\gamma_j=E[(y_t-\mu)(y_{t-j}-\mu)]$ denote population autocovariance, where $\mu$ is population mean of $y_t$, assuming covariance-stationary. Then, $\gamma_j$ goes to $0$ as $j$ goes to $\infty$.

I have been trying to use algebra to prove $\gamma_j$ goes to $0$ for a while, but cannot figure it out. Could anyone give me a hint on how to understand this limiting behavior?